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Loss rates for Lévy processes with two reflecting barriers

Asmussen, Sören LU and Pihlsgård, Mats LU (2007) In Mathematics of Operations Research 32(2). p.308-321
Abstract
Let {Xt} be a Lévy process which is reflected at 0 and K>0. The reflected process {VtK} is constructed as VtK = V0K + Xt + Lt0 - LtK where{Lt0} and {LtK} are the local times at 0 and K, respectively. We consider the loss rate lK, defined by lK=E KL1K where E K is the expectation under the stationary measure K. The main result of the paper is the identification of lK in terms of K and the characteristic triplet of {Xt}. We also derive asymptotics of lK as K when EXt <0 and the Lévy measure of {Xt} is light-tailed.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Mathematics of Operations Research
volume
32
issue
2
pages
308 - 321
publisher
Informs
external identifiers
  • Scopus:38549160076
ISSN
0364-765X
DOI
10.1287/moor.1060.0226
language
English
LU publication?
yes
id
fc63aeee-e5f7-4d7b-9848-e938d3994489 (old id 930220)
alternative location
http://www.jstor.org/stable/25151791
date added to LUP
2008-01-15 15:07:55
date last changed
2017-01-01 08:00:51
@article{fc63aeee-e5f7-4d7b-9848-e938d3994489,
  abstract     = {Let {Xt} be a Lévy process which is reflected at 0 and K&gt;0. The reflected process {VtK} is constructed as VtK = V0K + Xt + Lt0 - LtK where{Lt0} and {LtK} are the local times at 0 and K, respectively. We consider the loss rate lK, defined by lK=E KL1K where E K is the expectation under the stationary measure K. The main result of the paper is the identification of lK in terms of K and the characteristic triplet of {Xt}. We also derive asymptotics of lK as K when EXt &lt;0 and the Lévy measure of {Xt} is light-tailed.},
  author       = {Asmussen, Sören and Pihlsgård, Mats},
  issn         = {0364-765X},
  language     = {eng},
  number       = {2},
  pages        = {308--321},
  publisher    = {Informs},
  series       = {Mathematics of Operations Research},
  title        = {Loss rates for Lévy processes with two reflecting barriers},
  url          = {http://dx.doi.org/10.1287/moor.1060.0226},
  volume       = {32},
  year         = {2007},
}